Chain tensor products and interval effect algebras
type: Item
instance of: scholarly article
title: Chain tensor products and interval effect algebras
zbMATH Open document ID: 0884.03060
DOI: 10.1007/BF02435802
published in: International Journal of Theoretical Physics
publication date: 1998-03-17T00:00:00Z
review text: An effect algebra is an algebra \(P= (P,\oplus,0,1)\), where \(\oplus\) is a partial binary operation which is commutative and associative, given \(a\in P\) there is a unique element \(a'\) in \(P\) such that \(a \oplus a'= 1, \) and if \( a \oplus 1\) is defined, then \(a= 0.\) The tensor product of D-posets (an equivalent structure) has been introduced by the reviewer [``Tensor product of difference posets'', Trans. Am. Math. Soc. 347, 1043-1057 (1995; Zbl 0859.03031)]. Nowadays it is known that there are stateless effect algebras for which there is no tensor product [\textit{S. Gudder} and \textit{R. Greechie}, ``Effect algebra counterexamples'', Math. Slovaca 46, 317-325 (1996)]. The author of the present article introduces a chain tensor product and normal interval effect algebras (including, e.g., Hilbert space effect algebras), and he studies relations among them.
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 08A55
zbMATH DE Number: 1066037
zbMATH Keywords: effect algebra
zbMATH Keywords: tensor product
zbMATH Keywords: chain tensor product
zbMATH Keywords: interval effect algebra
author: Stan Gudder
reviewed by: Anatolij Dvurečenskij
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1066037